Radio is very different from the end user who plays the same song 1000 times because it’s in his play list.
Not sure that one user playing a song 1000 times is any more liable for royalty payments to an artist than a radio station playing that song once to 10,000 listeners - perhaps the reverse in fact.
I don't know about US practice, but certainly in the UK, radio stations pay a huge sum to the recording artists agency (forgotten its exact title) so playing on the radio is good for the artist both for promoting his work and for earning him a bit of cash. Are you saying that US radio stations pay nothing?